• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

sgbcon - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,

SYNOPSIS

  SUBROUTINE SGBCON( NORM, N, NSUB, NSUPER, A, LDA, IPIVOT, ANORM, 
 *      RCOND, WORK, WORK2, INFO)
  CHARACTER * 1 NORM
  INTEGER N, NSUB, NSUPER, LDA, INFO
  INTEGER IPIVOT(*), WORK2(*)
  REAL ANORM, RCOND
  REAL A(LDA,*), WORK(*)

  SUBROUTINE SGBCON_64( NORM, N, NSUB, NSUPER, A, LDA, IPIVOT, ANORM, 
 *      RCOND, WORK, WORK2, INFO)
  CHARACTER * 1 NORM
  INTEGER*8 N, NSUB, NSUPER, LDA, INFO
  INTEGER*8 IPIVOT(*), WORK2(*)
  REAL ANORM, RCOND
  REAL A(LDA,*), WORK(*)

F95 INTERFACE

  SUBROUTINE GBCON( NORM, [N], NSUB, NSUPER, A, [LDA], IPIVOT, ANORM, 
 *       RCOND, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: NORM
  INTEGER :: N, NSUB, NSUPER, LDA, INFO
  INTEGER, DIMENSION(:) :: IPIVOT, WORK2
  REAL :: ANORM, RCOND
  REAL, DIMENSION(:) :: WORK
  REAL, DIMENSION(:,:) :: A

  SUBROUTINE GBCON_64( NORM, [N], NSUB, NSUPER, A, [LDA], IPIVOT, 
 *       ANORM, RCOND, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: NORM
  INTEGER(8) :: N, NSUB, NSUPER, LDA, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
  REAL :: ANORM, RCOND
  REAL, DIMENSION(:) :: WORK
  REAL, DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void sgbcon(char norm, int n, int nsub, int nsuper, float *a, int lda, int *ipivot, float anorm, float *rcond, int *info);

void sgbcon_64(char norm, long n, long nsub, long nsuper, float *a, long lda, long *ipivot, float anorm, float *rcond, long *info);

PURPOSE

sgbcon estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGBTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as

   RCOND = 1 / ( norm(A) * norm(inv(A)) ).

ARGUMENTS

• NORM (input)
  Specifies whether the 1-norm condition number or the infinity-norm condition number is required:

   = '1' or 'O':  1-norm;

   = 'I':         Infinity-norm.

• N (input)
  The order of the matrix A. N > = 0.

• NSUB (input)
  The number of subdiagonals within the band of A. NSUB > = 0.

• NSUPER (input)
  The number of superdiagonals within the band of A. NSUPER > = 0.

• A (input)
  Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with NSUB+NSUPER superdiagonals in rows 1 to NSUB+NSUPER+1, and the multipliers used during the factorization are stored in rows NSUB+NSUPER+2 to 2*NSUB+NSUPER+1.

• LDA (input)
  The leading dimension of the array A. LDA > = 2*NSUB+NSUPER+1.

• IPIVOT (input)
  The pivot indices; for 1 < = i < = N, row i of the matrix was interchanged with row IPIVOT(i).

• ANORM (input)
  If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.

• RCOND (output)
  The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

• WORK (workspace)
  dimension(3*N)

• WORK2 (workspace)
  dimension (N)

• INFO (output)
  

   = 0:  successful exit

   < 0: if INFO  = -i, the i-th argument had an illegal value